Abstract: Ethene polymerization by Phillips catalysis is carried out using (1) a supported catalyst, which is laden with chromium, phosphorus and aluminum, and (2) a cocatalyst, (1) being obtained by a method in which (1.1) a catalyst intermediate laden with chromium, phosphorus and aluminum is prepared from a silicate carrier, a selected chromium compound, a selected phosphorus compound and a selected aluminum compound, and then (1.2) the catalyst intermediate is heated in an oxygen-containing gas stream. In this process, the component (1) used is one which is obtained by a method in which, in each case in a specific manner, (1.1) in a first stage, (1.1.1) first a suspension is prepared from (1.1.1.1) a finely divided silicate carrier and (1.1.1.2) an inert organic solvent, (1.1.2) then, (1.1.2.1) in an inert organic solvent, (1.1.2.2) an organic chromium compound is combined with (1.1.2.3) an aluminum trialkyl, (1.1.3) then (1.1.3.1) the suspension resulting from (1.1.1) is combined with (1.1.3.